Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C53 · Schur multiplier (H2) = C24 |
| direct product | C53×#26995 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C53 |
| prime radical | C53×#537 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C22×C4×C53 ◁ G | |
762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,22)(12,17)(13,28)(14,20)(15,21)(16,24)(18,29)(19,26)(23,37)(25,32)(27,31)(30,35)(33,39)(34,38)(36,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,4,8)(2,5,6,7)(9,11,14,24,15,12,26,25)(10,16,19,22,21,32,20,17)(13,23,29,38,30,27,40,39)(18,31,28,34,36,37,35,33);(2,6)(3,8)(9,12)(10,17)(11,15)(13,23)(14,25)(16,19)(18,34)(20,32)(21,22)(24,26)(27,30)(28,37)(29,38)(31,35)(33,36)(39,40);(2,6)(5,7)(9,13,26,40,15,30,14,29)(10,18,20,35,21,36,19,28)(11,23,25,39,12,27,24,38)(16,31,17,33,32,37,22,34)2120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 19983);